Contractivity properties of Ornstein-Uhlenbeck semigroup for general commutation relations |
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Authors: | Email author" target="_blank">Ilona?KrolakEmail author |
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Institution: | (1) Institute of Mathematics, Wrocław University, pl.Grunwaldzki 2/4, 50-384 Wrocław, Poland |
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Abstract: | We study a certain class of von Neumann algebras generated by selfadjoint elements ωi=ai+ai+, where ai, ai+ satisfy the general commutation relations: We assume that operator T for which the constants are matrix coefficients satisfies the braid relation. Such algebras were investigated in BSp] and K] where the positivity of the Fock representation and factoriality were shown. In this paper we prove that T-Ornstein-Uhlenbeck semigroup Ut=ΓT(e−t), t>0 arising from the second quantization procedure is hyper- and ultracontractive. The optimal bounds for hypercontractivity are also discussed.This paper was partially supported by KBN grant no 2P03A00732 and also by RTN grant HPRN-CT-2002-00279. |
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Keywords: | 81S05 46L65 |
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